factor the polynomial expression completely: 8x^3-27
We can factor the polynomial expression 8x^3 - 27 using the difference of cubes formula, which states that a^3 - b^3 = (a - b)(a^2 + ab + b^2).
In this case, we have a = 2x and b = 3, so we can write the expression as:
8x^3 - 27 = (2x)^3 - 3^3
= (2x - 3)((2x)^2 + (2x)(3) + (3)^2)
= (2x - 3)(4x^2 + 6x + 9)
So, the polynomial expression 8x^3 - 27 is completely factored as (2x - 3)(4x^2 + 6x + 9).